Built in 1924, the fully-renovated home spans 1,065 square feet, has hardwood floors, high ceilings, an open floor plan, a front courtyard with a fountain and a detached guest unit. It’s hidden behind walls, hedges and an electric security gate, making it, “extremely private,” according to the listing with Cynthia Land or Rodeo Realty, who did not immediately respond to requests for comment.

Mr. Duvall—who played the consigliere of the Corleone family in “The Godfather” and “The Godfather: Part II,” and starred in “To Kill a Mockingbird,” and “Apocalypse Now” —won’t be moving far. According to reports, he has owned another property nearby since 2005 and has a three-story Georgian farmhouse set on 362 acres in The Plains, Virginia, that has been featured in Architectural Digest.